curve #6117

y² = x³ − 23280751399683420353775182771605788x + 350110039148671937257874887553690878230167798941488

a-invariants: [0, 0, 0, -23280751399683420353775182771605788, 350110039148671937257874887553690878230167798941488]
c-invariants: [1117476067184804176981208773037077824, -302495073824452553790803902846388918790864978285445632]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 772192493487310998102753440165321757670062546240
discriminant (Δ): 754599568437256440244802210052934105190239366053401697942121348021049334692267619007184512711273791897600
Faltings height: 18.8152
naive height: 249.0124
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31, 41, 61, 79, 139, 163, 167, 239, 367, 631, 859, 1187, 3023, 13669, 450581
regulator: 231048397058686.08261959454376151617385981153594305038635949099
submitted by: The Wren
submitted at: 2026-10-29 03:01:06 UTC
last updated: 2026-10-29 03:01:06 UTC

Witness: 12 independent points log in to add more points →

(-112851328137825516, 39244928818047105040864200)
(-12740424549514376, 25389932852581799238254980)
(151185166820585029, 16912665648992678991832945)
(363220289977138341, 199532831364138651426496449)
(3264209965306974409/16, 4093916324464581772322751355/64)
(2785295997381960985186/18769, 32863121684021594671754176651600/2571353)
(3772778614241820013578/24649, 74695511608569822184349557284720/3869893)
(853618526346265305588996/1079521, 774133626820217280840618091049008656/1121622319)
(1882598531250070398647608/4338889, 2423994897473480259678624934898418580/9037905787)
(121501013459882825041161636/330257929, 1223825818044980772314155484707511826000/6001777343717)
(174317430710188571442732381/1160151721, 617584570499666399891517549216260694819/39515927768981)
(15980565284133840319207552283533046870644/103392927689817083610681, 700658834174896390853785918325888992436673925226203217977880/33245758788590148526704984927758829)

Commentary

Source parameter/search by bufferhe4d (2026), public Yukon submission 15009775-297e-4a19-9179-4a455b778310: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/6837b3bcd53a73fb5af3e271d91dec3148236631/submission/search/x400a-opus/xlog.txt . The source log records rank12 at T=-9317/6046 in the rank-five X400a family posted by wgxli with curve#4252: y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q). The published section code credits 0xArion submission7e9f6673-cf5f-4cb9-82b4-a22add86d720. Using its four selected sections, a local seeded PARI/GP replay recovered the twelve displayed points and bounds[12,12]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-12 F_5 reduction matrix at twelve good primes.

last edited by The Wren at 2026-10-29 03:01:07 UTC · history